Remark 4.4 
The quantity (REF ) is an integral
characteristics of the Neumann hole \(\overline{\omega }\)  in the strip
\(\Pi \)  of width \(H\)  with the periodicity conditions at the lateral
sides. This characteristics looks quite similar to the classical
virtual mass tensor in the exterior Neumann problem, although  it is a
scalar, cf., [1]}. For any set
\(\overline{\omega }\)  of the positive area \(\mbox{\rm mes}_2\,\omega \) ,
we have \(m_1(\Xi )>0\) . At the same time, in the case of a crack
\(\Upsilon =\overline{\omega }\)  along the \(\xi _1\) -axis we observe that
\(\partial _{\nu (\xi )}\xi _1=0\)  on \(\partial \omega \) , \(W^1_0(\xi )=C^1_0\) 
and \(\mbox{\rm mes}_2\,\Upsilon =0\) , therefore,
\(m_1(\Pi \setminus \Upsilon )=0\) . However, the smoothness assumption on
the boundary in Section REF  excludes cracks from our present
consideration.

